Honorable

Recently my cousin's Dell Inspiron 546 has started to have problems. The screen has gone very dark, we tried playing with the settings, no change. Tried a different monitor, no change. This has led me to the conclusion that the graphics card is bad. Nothing on the computer has been changed since purchase.
I'm really not sure as to what I need to know when doing this or how to obtain the information I need. The only things I know of are that I need to make sure there is room for the card, it's interface is compatible, it does not generate too much heat, and it gets the right amount of power. I understand that the PSU is a limiting factor, as well as space inside the case. Other than that I am a bit lost.
What I would like to know is: What is the best video card it can take without upgrading the PSU? What is the best graphics card it can take with an upgrade to the PSU? And what is a good brand/model of PSU that will work with this system? As fas as price goes, we'd like to keep it below $250(but we'd like to know our overall options.) At this point no upgrades are planned, but will be in the future, of course. This isn't going to be used for any high-end games of any sort. Case modification is not an option, so I would assume that would play a factor in the choice of card, considering heat. The motherboard would also never be upgraded.
Any help would be greatly appreciated. I hope the information provided is enough, if not, let me know.